The present invention relates to seismic data processing, and more particularly to a more rapid method of migrating seismic data for steeply-dipping reflectors and large lateral variations in velocity.
Typically, seismic data is arranged in arrays representing an acoustic signal received by sensors. Often the seismic data represents signal values as a function of geometric location and frequency content of the signal. Geological sensors, like geophones and hydrophones, measure the wavefields at a multitude of positions. The measured seismic data characterized by wavefields are processed to identify useful geological formations. One such processing step is called seismic data migration.
Seismic data migration requires solving the wave equation in the earth volume. Measured wavefield data points are used in conjunction with the wave equation to identify useful geological formations. It is well known in the art that the seismic data requires migration in order to restore the apparent positions of reflections to their correct locations (Claerbout1, 1999; Stolt and Benson2, 1986). Numerous techniques of seismic data migration are known in the art (Bording and Lines3, 1997; Claerbout4, 1999; Stolt and Benson5, 1986). Different techniques provide differing degrees of accuracy. In general, more accurate methods require greater computational resources. In order to use available computer resources in a cost-effective manner, computation-intensive algorithms must be designed as efficiently as possible.
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Conventional finite difference methods of migration are valued for their accuracy, but they are computationally intensive. Because of its expense, the finite difference method is most appropriate for use in regions where the acoustic signal velocity strongly varies laterally, as well as with depth (or time).
Most conventional finite difference methods of migration represent xe2x80x9cone-wayxe2x80x9d approximations of the two-way acoustic wave equation for constant density, which has the form:
∂2P/∂x2+∂2P/∂y2+∂2P/∂z2=(1/c2)∂2P/∂t2xe2x80x83xe2x80x83(1)
where
P=acoustic pressure,
x, y, z=position coordinates, and
c=acoustic velocity
Examples of known methods of finite difference solutions for the xe2x80x9ctwo-wayxe2x80x9d wave equation can be found, for example, in Bording and Lines6, 1997, and Smith, U.S. Pat. No. 5,999,488. These methods are particularly slow, since they independently account for downgoing and upgoing propagation of the wavefield. In addition, in order to use equation (1) effectively, the spatial distribution of the velocity, C(x,y,z), must be known very precisely. This level of precision is difficult to obtain. Thus, there is a long felt need for a method and system to retain the accuracy of the finite difference method at increased speed and reduced cost, without having a highly detailed knowledge of the spatial distribution for the propagation velocity.
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